The former Roma star is looking likely to leave St Mary's before the winter window shuts in just over three days' time after he was involved in a training ground incident that reportedly involved him attacking teammate Jose Fonte.
Osvaldo was subsequently suspended by the Premier League club for two weeks with manager Mauricio Pochettino conceding that he "doesn't know" if the 28-year-old will still be part of his squad at the start of February.
Serie A leader Juve is interested in taking the controversial forward back to Italy, initially on loan with a view to a permanent deal in the summer.
Any potential move for Osvaldo is likely to hinge on the immediate future of Mirko Vucinic, however, with the Montenegro international keen to leave Turin having struggled for regular playing time under Antonio Conte.
Juve is keen to resurrect the mooted swap deal for Inter midfielder Fredy Guarin after talks had broken down following a backlash from furious Nerazzurri fans who do not want to see one of the club's prized assets depart.
Goal understands a meeting has been scheduled to renegotiate the deal, with a potential Vucinic exit clearing the path for Osvaldo to make the move to the Turin club.
Conte's Juve currently sits at the top of the Serie A table and has been drawn against Trabzonspor in the last 32 of the Europa League, a competition Osvaldo would be eligible to feature in.